Hybrid subconvexity bounds for twists of $\mathrm{GL}(3)$ $L$-functions

Abstract

Let $\pi$ be a $SL(3,\mathbb{Z})$ Hecke-Maass cusp form and $\chi$ a primitive Dirichlet character of prime power conductor $\mathfrak{q}=p^k$ with $p$ prime. In this paper we will prove the following subconvexity bound $$L\left(\frac{1}{2}+it,\pi \times \chi \right){\ll }_{\pi ,\epsilon }{p}^{3/4}(\mathfrak{q}(1+|t|){)}^{3/4-3/40+\epsilon },$$ for any $\epsilon >0$ and $t\in \mathbb{R}$.

arXiv admin note: text overlap with arXiv:2108.09410, arXiv:2110.08682 by other authors